It is well-known (see, e.g., [1]}, [2]}) that problem \((SP)\)  possesses a uniques solution which is exactly the saddle point of the corresponding energy functional
\(\mathcal {E}:X\times \Lambda \rightarrow \mathbb {R}\) ,
\(\mathcal {E}(v,\mu ):=\frac{1}{2}a(v,v)+b(v,\mu )-(f,v),\) 
i.e.
\(\mathcal {E}(u,\mu ) \le \mathcal {E}(u,\lambda ) \le \mathcal {E}(v,\lambda ), \ \; \forall v\in X,\ \forall \mu \in \Lambda ,\) 
